Question

The correlation matrix obtained for the variables bp (y) (blood pressure), age (x1) (age), smk (x2) (smoke) and WET(X3) (Weight), is given by:
BP AGE SMK WET
BP 1 0.64 0.72 0.48
AGE 1 0.32 0.78
SMK 1 0.40
WET 1
Based on this matrix please calculate the partial correlation.
a. 0.53
b. 0.48
c. 0.62
d. 0.32

Answer 1

Answer:

c) 0.62

Step-by-step explanation:

In this case, we are required to find the partial correlation, $r_Y_X_1_|_X_2$.

To find the partial correlation, use the formula:

$r_Y_X_1_|_X_2 = \frac{r_Y_X_1 - r_Y_X_2 * r_X_1_X_2}{\sqrt{1 - r_X_1_X_2}^2 - \sqrt{1 - r_Y_X_2}^2}$

$r_Y_X_1_|_X_2 = \frac{0.64 - 0.72 * 0.32}{\sqrt{1 - 0.32}^2 - \sqrt{1 - 0.72}^2}$

$= \frac{0.410}{0.657}$

$r_Y_X_1_|_X_2 = 0.62$

The partial correlation is 0.62.

Option C